A task involving the equivalence between fractions, percentages and
decimals which depends on members of the group noticing the needs
of others and responding.

Which Solid?

Stage: 2, 3 and 4 Challenge Level:

This
is one of a series of problems designed to develop learners' team
working skills. Other tasks in the series can be found by going to
thisarticle.

What are you aiming to do?

For the task:

One member of the team is
trying to find out what is on their chosen card (the unknown) by
asking as few questions as possible.

The rest of the team need
to confer and agree on a "Yes" or "No" answer to each question the
person asks, and keep track of the number of questions that have
been asked in total.

As a team:

asking questions - making sense of your own understanding

being concise

listening

reflecting on what has been said.

Getting started

The task is designed to
work with a team of four or five people. If you do the task several
times, members of the team can take turns at trying to find the
unkown solid. You may also wish to appoint an observer.

You will need the set of solids cards.
Spread them out on the table so that everyone can see the solids
chosen for this task.

You will each need a
sheet of paper and pencil.

Tackling the problem

Rules

Choose someone on the team to keep track of the number of
questions - this might be the observer.

The person who has been chosen to try to find the unknown solid
chooses a card and hands it to the rest of the team without looking
at it.

The person trying to find which solid can ask up to 8
questions.

When a question has been asked, each of the other members of
the team writes "Yes" or "No" on their sheet of paper. If they all
agree one person gives the answer.

If the team do not agree, they will need to confer - preferably
out of earshot of the person trying to find the solid. Once in
agreement, one person gives the answer.

The person trying to find the unknown can have at most two
attempts at guessing what is on the card before the task ends. Each
guess counts as one of the 8 questions.

The team can offer the hint "Cold" or "Warm" or "Hot" if the
first guess is incorrect.

At the end of the task
the team should discuss what proved to be good questions and less
good questions. If the person does not identify what is on the
card, discuss what questions might have worked more
effectively.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.